I would recommend ZenDesk.
But if a dissatisfied customer sends an email to the Support, there is no way to avoid your personel seeing that. If the complaint is called in, whish they usually are, then you need to implement a process to forward those calls to the responsible manager.

1st Post

Hello,
Speaking about issue tracking software solutions I would recommend you Comindware Tracker. I’ve started using it not so long ago. It has met with my requirements: flexible, functional, fast, interactive, simple, user-friendly and reasonably priced. So, hope it will be as useful for you as for me.
Best regards